Actually, that's nonsense. Even if you are employing the narrowest of supposedly rational methods to establish the veracity of a theory, you have to start with certain assumptions.
I'm not going to assume you understand how science works since you show signs of not understanding the basics. When a scientist creates a hypothesis they have to make a prediction and then design a test. It has to be based on observations, facts, and ALL data collected. Scientists don't get to pick and choose their facts and data, they HAVE to account for all of it. The scientific method requires the fewest possible assumptions, and this is the sake of objectivity. What assumptions do empirisists use? That our senses work reliably. That the laws of nature are constant, like gravity and the decay rates of radioactive isotopes. What are not used? Like a God exists. That there is a divinity at work. Etc.
Many hypotheses fail to meet the 99.95% statistical minimum in testing, but might still be viable as an explanation for observations. A scientist can redesign the test to eliminate certain uncontrollable variables. The approach here is to control variables so the conclusions have fewer alternative influences, and this includes assumptions. If science assumes a God, then the conclusion will include a God, and as we all know, gods are not known to exist.
If you begin with the assumption that a given proposition cannot possibly be true under any circumstances, then of course all your considerations will lead you nowhere.
False, it will help you understand what is true. Why? The same reason that in law a suspect of a crime is presumed innocent and evidence is used to demonstrate guilt. BTW, no one is saying that your religious assumptions can't possible be true. That is a straw man on your part.
In logic the natural default for any proposition is that it is untrue, and the claimant has to demonstrate their claim IS true by using evidence. This is why believers fail to persuade critical thinkers, they have claims they believe are true but lack evidence that their beliefs ARE true or even likely true. If a child claims the Tooth Fairy exists, do you automatically assume the kid is correct? Who knows, maybe the kid has had an experience, and he shows you the dollar he got for his tooth. That's pretty solid evidence. The kid left a tooth under his pillow and sure enough there was a dollar in its place the next morning. What better explanation is there, it must be the Tooth Fairy.